Pub Date : 2021-03-17DOI: 10.21203/RS.3.RS-379917/V1
Joseph Omolo
This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC)interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specied by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counter-rotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specied by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-eld state je0i is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state je0i into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-eld state jg0i is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state jg0i into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states je0i , jg0i to corresponding n 0 entangled eigenstates j+en i , j g ni of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, eld mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF, CRF, but each evolves with time in the alternate frame.
这篇文章是对持续假设的回应，甚至在最近的实验突破和理论方法进展的报告和评论中也被引用，即反杰恩斯-卡明斯(AJC)相互作用是量子拉比模型(QRM)中难以处理的能量非守恒组成部分。我们提出了QRM动力学的三个关键特征:(a) AJC相互作用分量具有一个守恒激励数算子，并且是精确可解的;(b) QRM动力学空间由一个以产生RF的U(1)对称性的守恒JC激励数算子指定的精确解Jaynes-Cummings (JC)相互作用为主导的旋转坐标系(RF)和一个以产生U(1)对称性的守恒AJC激励数算子指定的精确解反Jaynes-Cummings (AJC)相互作用为主导的相关逆旋转坐标系(CRF)组成RF中QRM动力学演化的U(1)对称性，初始原子场态je0i是有效AJC哈密顿量HAJC的特征态，而有效JC哈密顿量HJC将该初始态je0i驱动为时间演化的纠缠态，在相应的CRF中QRM动力学演化过程中，初始原子场态jg0i是有效JC哈密顿量的特征态。而有效的AJC哈密顿量将这个初始状态jg0i驱动到一个时间演化的纠缠态，从而解决了理论和实验QRM动力学的长期挑战之一;将初始态je0i, jg0i分别推广到RF中AJC和CRF中JC对应的n个纠缠本征态j+en i, jg ni，提供了QRM在原子、场模式、初始光子数较大的JC和AJC激发数的时间演化中以坍缩和恢复为特征的一般动力学演化;JC和AJC激励数在各自的帧RF、CRF中保持不变，但在交替帧中随时间而变化。
{"title":"The anti-Jaynes-Cummings model is solvable : quantum Rabi model in rotating and counter-rotating frames ; following the experiments","authors":"Joseph Omolo","doi":"10.21203/RS.3.RS-379917/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-379917/V1","url":null,"abstract":"\u0000 This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC)interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specied by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counter-rotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specied by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-eld state je0i is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state je0i into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-eld state jg0i is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state jg0i into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states je0i , jg0i to corresponding n 0 entangled eigenstates j+en i , j g ni of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, eld mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF, CRF, but each evolves with time in the alternate frame.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89489392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. C¸ . is supported by the BAGEP Award of the Science Academy and by the Research Fund of Bah¸ce¸sehir University (BAUBAP) under project no: BAP.2019.02.03. S.D. acknowledges support from the U.S. National Science Foundation under Grant No. DMR-2010127. This research was supported by grant number FQXi-RFP-1808 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation (SD).
B.正确。得到了中国科学院BAGEP奖和德国约德大学科研基金(BAUBAP)的资助，项目号:baap .2019.02.03。S.D.感谢美国国家科学基金会的资助。dmr - 2010127。本研究由Foundation Questions Institute和硅谷社区基金会(SD)的捐款人建议基金Fetzer Franklin Fund资助，资助号为FQXi-RFP-1808。
{"title":"Second law of thermodynamics for quantum correlations","authors":"Akram Touil, B. cCakmak, Sebastian Deffner","doi":"10.13016/M2RSDW-ZGPS","DOIUrl":"https://doi.org/10.13016/M2RSDW-ZGPS","url":null,"abstract":"B. C¸ . is supported by the BAGEP Award of the Science Academy and by the Research \u0000Fund of Bah¸ce¸sehir University (BAUBAP) under project no: BAP.2019.02.03. S.D. \u0000acknowledges support from the U.S. National Science Foundation under Grant No. \u0000DMR-2010127. This research was supported by grant number FQXi-RFP-1808 from \u0000the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund \u0000of Silicon Valley Community Foundation (SD).","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"133 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77517075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-26DOI: 10.1103/PhysRevA.103.062408
J. Fiurášek, Robert Stárek, M. Mičuda
We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of the filtering and the optimal filters are those that maximize the overall success probability. We discuss in detail the case of symmetric real filters and extend our analysis also to asymmetric and complex filters.
{"title":"Optimal implementation of two-qubit linear-optical quantum filters","authors":"J. Fiurášek, Robert Stárek, M. Mičuda","doi":"10.1103/PhysRevA.103.062408","DOIUrl":"https://doi.org/10.1103/PhysRevA.103.062408","url":null,"abstract":"We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of the filtering and the optimal filters are those that maximize the overall success probability. We discuss in detail the case of symmetric real filters and extend our analysis also to asymmetric and complex filters.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90458850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-01DOI: 10.21203/RS.3.RS-174871/V1
Ravo Tokiniaina Ranaivoson, R. Andriambololona, Rakotoson Hanitriarivo
The main purpose of this work is to identify the general quadratic operator which is invariant under the action of Linear Canonical Transformations (LCTs). LCTs are known in signal processing and optics as the transformations which generalize certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the canonical commutation relations characterizing the coordinates and momenta operators. In this paper, LCTs corresponding to a general pseudo-Euclidian space are considered. Explicit calculations are performed for the monodimensional case to identify the corresponding LCT invariant operator then multidimensional generalizations of the obtained results are deduced. It was noticed that the introduction of a variance-covariance matrix, of coordinate and momenta operators, and a pseudo-orthogonal representation of LCTs facilitate the identification of the invariant quadratic operator. According to the calculations carried out, the LCT invariant operator is a second order polynomial of the coordinates and momenta operators. The coefficients of this polynomial depend on the mean values and the statistical variances-covariances of these coordinates and momenta operators themselves. The eigenstates of the LCT invariant operator are also identified with it and some of the main possible applications of the obtained results are discussed.
{"title":"Invariant quadratic operator associated with Linear Canonical Transformations","authors":"Ravo Tokiniaina Ranaivoson, R. Andriambololona, Rakotoson Hanitriarivo","doi":"10.21203/RS.3.RS-174871/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-174871/V1","url":null,"abstract":"The main purpose of this work is to identify the general quadratic operator which is invariant under the action of Linear Canonical Transformations (LCTs). LCTs are known in signal processing and optics as the transformations which generalize certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the canonical commutation relations characterizing the coordinates and momenta operators. In this paper, LCTs corresponding to a general pseudo-Euclidian space are considered. Explicit calculations are performed for the monodimensional case to identify the corresponding LCT invariant operator then multidimensional generalizations of the obtained results are deduced. It was noticed that the introduction of a variance-covariance matrix, of coordinate and momenta operators, and a pseudo-orthogonal representation of LCTs facilitate the identification of the invariant quadratic operator. According to the calculations carried out, the LCT invariant operator is a second order polynomial of the coordinates and momenta operators. The coefficients of this polynomial depend on the mean values and the statistical variances-covariances of these coordinates and momenta operators themselves. The eigenstates of the LCT invariant operator are also identified with it and some of the main possible applications of the obtained results are discussed.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"16 9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90025062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-28DOI: 10.1103/PhysRevA.103.063707
D. Na, Jie Zhu, W. Chew
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.
{"title":"Diagonalization of the Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode decomposition","authors":"D. Na, Jie Zhu, W. Chew","doi":"10.1103/PhysRevA.103.063707","DOIUrl":"https://doi.org/10.1103/PhysRevA.103.063707","url":null,"abstract":"We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"288 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72566860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-27DOI: 10.21203/RS.3.RS-149814/V1
S. Łukaszyk
The Extended Wigner’s Friend thought experiment comprising a quantum system containing an agent who draws conclusions, upon observing the outcome of a measurement of a qubit prepared in two non-orthogonal versions by another agent led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to coherent entangled state (Bell type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend invalidates such equivalency. It is also argued that the assumption of locality (physical space) introduces superfluous identity of indiscernibles metric axiom, which is invalid in quantum domain and generally disproven by the Ugly duckling mathematical theorem.
{"title":"Making Mistakes Saves the Single World of the Extended Wigner’s Friend Experiment","authors":"S. Łukaszyk","doi":"10.21203/RS.3.RS-149814/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-149814/V1","url":null,"abstract":"\u0000 The Extended Wigner’s Friend thought experiment comprising a quantum system containing an agent who draws conclusions, upon observing the outcome of a measurement of a qubit prepared in two non-orthogonal versions by another agent led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to coherent entangled state (Bell type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend invalidates such equivalency. It is also argued that the assumption of locality (physical space) introduces superfluous identity of indiscernibles metric axiom, which is invalid in quantum domain and generally disproven by the Ugly duckling mathematical theorem.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88401681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-17DOI: 10.1590/1806-9126-rbef-2020-0422
S. Vincenzo
In the one-dimensional Klein-Fock-Gordon theory, the probability density is a discontinuous function at the point where the step potential is discontinuous. Thus, the mean value of the external classical force operator cannot be calculated from the corresponding formula of the mean value. To resolve this issue, we obtain this quantity directly from the Klein-Fock-Gordon equation in Hamiltonian form, or the Feshbach-Villars wave equation. Not without surprise, the result obtained is not proportional to the average of the discontinuity of the probability density but to the size of the discontinuity. In contrast, in the one-dimensional Schr"odinger and Dirac theories this quantity is proportional to the value that the respective probability density takes at the point where the step potential is discontinuous. We examine these issues in detail in this paper. The presentation is suitable for the advanced undergraduate level.
{"title":"On the mean value of the force operator for 1D particles in the step potential.","authors":"S. Vincenzo","doi":"10.1590/1806-9126-rbef-2020-0422","DOIUrl":"https://doi.org/10.1590/1806-9126-rbef-2020-0422","url":null,"abstract":"In the one-dimensional Klein-Fock-Gordon theory, the probability density is a discontinuous function at the point where the step potential is discontinuous. Thus, the mean value of the external classical force operator cannot be calculated from the corresponding formula of the mean value. To resolve this issue, we obtain this quantity directly from the Klein-Fock-Gordon equation in Hamiltonian form, or the Feshbach-Villars wave equation. Not without surprise, the result obtained is not proportional to the average of the discontinuity of the probability density but to the size of the discontinuity. In contrast, in the one-dimensional Schr\"odinger and Dirac theories this quantity is proportional to the value that the respective probability density takes at the point where the step potential is discontinuous. We examine these issues in detail in this paper. The presentation is suitable for the advanced undergraduate level.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82126841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1103/PHYSREVA.103.033513
T. Ramos, J. Garc'ia-Ripoll, D. Porras
We present a topological approach to the input-output relations of photonic driven-dissipative lattices acting as directional amplifiers. Our theory relies on a mapping from the optical non-Hermitian coupling matrix to an effective topological insulator Hamiltonian. This mapping is based on the singular value decomposition of non-Hermitian coupling matrices, whose inverse matrix determines the linear input-output response of the system. In topologically non-trivial regimes, the input-output response of the lattice is dominated by singular vectors with zero singular values that are the equivalent of zero-energy states in topological insulators, leading to directional amplification of a coherent input signal. In such topological amplification regime, our theoretical framework allows us to fully characterize the amplification properties of the quantum device such as gain, bandwidth, added noise, and noise-to-signal ratio. We exemplify our ideas in a one-dimensional non-reciprocal photonic lattice, for which we derive fully analytical predictions. We show that the directional amplification is near quantum-limited with a gain growing exponentially with system size, $N$, while the noise-to-signal ratio is suppressed as $1/sqrt{N}$. This points out to interesting applications of our theory for quantum signal amplification and single-photon detection.
{"title":"Topological input-output theory for directional amplification","authors":"T. Ramos, J. Garc'ia-Ripoll, D. Porras","doi":"10.1103/PHYSREVA.103.033513","DOIUrl":"https://doi.org/10.1103/PHYSREVA.103.033513","url":null,"abstract":"We present a topological approach to the input-output relations of photonic driven-dissipative lattices acting as directional amplifiers. Our theory relies on a mapping from the optical non-Hermitian coupling matrix to an effective topological insulator Hamiltonian. This mapping is based on the singular value decomposition of non-Hermitian coupling matrices, whose inverse matrix determines the linear input-output response of the system. In topologically non-trivial regimes, the input-output response of the lattice is dominated by singular vectors with zero singular values that are the equivalent of zero-energy states in topological insulators, leading to directional amplification of a coherent input signal. In such topological amplification regime, our theoretical framework allows us to fully characterize the amplification properties of the quantum device such as gain, bandwidth, added noise, and noise-to-signal ratio. We exemplify our ideas in a one-dimensional non-reciprocal photonic lattice, for which we derive fully analytical predictions. We show that the directional amplification is near quantum-limited with a gain growing exponentially with system size, $N$, while the noise-to-signal ratio is suppressed as $1/sqrt{N}$. This points out to interesting applications of our theory for quantum signal amplification and single-photon detection.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90704153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1103/PHYSREVA.103.042214
M. Mohammady
The Two-Point energy Measurement (TPM) protocol defines the work done on a system undergoing unitary evolution as the difference in energy measurement outcomes performed before and after such evolution. By noting that energy measurements on the system can be modelled as a unitary premeasurement interaction between the system and a measurement apparatus, followed by measurement of the apparatus by a pointer observable, we show that it is possible to design a measurement scheme for the TPM protocol on the system that simultaneously acts as a TPM protocol for the compound of system-plus-apparatus so as to reveal the total work distribution. We further demonstrate that: (i) the average total work will be the change in average energy, given the total unitary evolution, for all initial system states and system unitary processes; and (ii) the total work distribution will be identical to the system-only work distribution, for all system states, if and only if the unitary premeasurements conserve the total energy of system-plus-apparatus for all system states.
两点能量测量(Two-Point energy Measurement, TPM)协议将在经历单一进化的系统上完成的工作定义为在这种进化之前和之后执行的能量测量结果的差异。通过注意到系统上的能量测量可以建模为系统和测量设备之间的一个统一的预测量相互作用，然后通过一个可观察的指针对设备进行测量，我们表明有可能为系统上的TPM协议设计一个测量方案，同时作为系统+设备复合的TPM协议，从而揭示总功分布。我们进一步证明:(i)对于所有初始系统状态和系统酉过程，给定总酉演化，平均总功将是平均能量的变化;并且(ii)对于所有系统状态，当且仅当统一预测量保留所有系统状态的系统加设备的总能量时，总功分布将与仅系统的功分布相同。
{"title":"Self-consistency of the two-point energy measurement protocol","authors":"M. Mohammady","doi":"10.1103/PHYSREVA.103.042214","DOIUrl":"https://doi.org/10.1103/PHYSREVA.103.042214","url":null,"abstract":"The Two-Point energy Measurement (TPM) protocol defines the work done on a system undergoing unitary evolution as the difference in energy measurement outcomes performed before and after such evolution. By noting that energy measurements on the system can be modelled as a unitary premeasurement interaction between the system and a measurement apparatus, followed by measurement of the apparatus by a pointer observable, we show that it is possible to design a measurement scheme for the TPM protocol on the system that simultaneously acts as a TPM protocol for the compound of system-plus-apparatus so as to reveal the total work distribution. We further demonstrate that: (i) the average total work will be the change in average energy, given the total unitary evolution, for all initial system states and system unitary processes; and (ii) the total work distribution will be identical to the system-only work distribution, for all system states, if and only if the unitary premeasurements conserve the total energy of system-plus-apparatus for all system states.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":"88 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78089252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-16DOI: 10.1103/PHYSREVRESEARCH.3.013244
Aleksandrina V. Kirkova, Weibin Li, P. Ivanov
We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition. We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cram'er-Rao bound for quantum oscillator at thermal equilibrium.
我们提出了一种绝热方法，利用捕获离子进行最佳声子温度估计，该方法可以在兰姆-迪克区之外运行。量子传感技术依赖于声子模式的时间依赖红边带跃迁，通常由非线性的Jaynes-Cummings模型描述。我们的传感技术的一个独特之处在于声子热分布的相关信息可以传递到集体自旋自由度上。我们表明，每个热态概率都绝热映射到各自的集体自旋激发构型上，因此温度估计只需在绝热跃迁结束时执行自旋相关的激光荧光测量即可进行。我们用Fisher信息描述了温度的不确定性，并证明了状态投影测量在热平衡状态下饱和了量子振荡器的基本量子Cram er rao界。
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